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Publisher’s version / la version de l'éditeur: International Journal of Offshore and Polar Engineering, 15, 2, pp. 125-131

An Operational Model of Iceberg DriftKubat, Ivana; Sayed, Mohamed; Savage, Stuart B.; Carrieres, Tom

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Implementation of the Canadian Ice Service Local Iceberg Drift Model

Ivana Kubat and Mohamed Sayed

Technical Report HYD-TR-042 April 2006


Ivana Kubat and Mohamed Sayed Canadian Hydraulics Centre

National Research Council of Canada Ottawa, Ont. K1A 0R6

Canada

Technical Report HYD-TR-042

April 2006

HYD-TR-042 i

ABSTRACT This report documents the computer code of an iceberg drift model intended for end-

users. The computer program keeps track of the dynamics, drift and deterioration of

individual icebergs. The code allows the user to access and modify the input and output

files. The users can thus incorporate information that may be locally available, which

may enhance the accuracy of the forecast. The model also makes it convenient for the

user to test various scenarios of environmental forcing and estimate the effect of

uncertainties regarding, for example, the iceberg geometry.

HYD-TR-042 i

HYD-TR-042 ii

TABLE OF CONTENTS

ABSTRACT .................................................................................................................................................... i TABLE OF CONTENTS ....................................................................................................................... ii

1. INTRODUCTION.................................................................................................................................. 1 2. ORGANIZATION OF THE PROGRAM .............................................................................................. 1

2.1 USER’s VARIABLES.......................................................................................................................... 2 Run parameters....................................................................................................................................... 2 Iceberg initial conditions ........................................................................................................................ 2 Environmental variables ......................................................................................................................... 3 Material properties.................................................................................................................................. 3

3. SUMMARY ........................................................................................................................................... 4 4. ACKNOWLEGEMENT......................................................................................................................... 4 APPENDIX A ................................................................................................................................................ 6 APPENDIX B................................................................................................................................................. 8

HYD-TR-042 i

HYD-TR-042 1


1. INTRODUCTION

A new iceberg drift, deterioration and calving model was developed by the Canadian Ice

Service (CIS) and National Research Council of Canada - Canadian Hydraulics Centre

(NRC/CHC). The model is described in detail in the Appendix A. One of the main

features of the new model is the utilization of detailed environmental forcing input, such

as the vertical profile of water current. The model runs on the CIS main computer system,

where it is linked to an ocean model and databases for other environmental inputs. The

output of the model has been in operational use by some end users (e.g. Provincial

Aerospace Ltd.) to predict the iceberg drift tracks over the Grand Banks. End users have

indicated an interest in the development of a version of the model that can be directly

operated in a stand-alone mode, without a need to link to the large ocean model and

databases at CIS. The idea is that the end user will have the ability to input iceberg and

environmental data into the model and could produce the output about the iceberg drift

whenever needed. Incorporation of local data and observations (i.e. real-time

measurements or user-defined observations of local conditions) would also result in

significantly better accuracy that will assist in decision making of iceberg towing. Such

model will be advantageous to the end-users as a great tool in predicting the iceberg drift.

The code incorporates an interface that gives the user a flexible ability to introduce the

initial conditions, environmental variables, and material properties. The user can also

customize the output to provide values of interest in any format and at the required

frequency. The input file allows the user to import values of water current, and wind

velocities. The user can also specify if the geometry of the iceberg is tabular or non-

tabular. For non-tabular icebergs, the user can override default values and specify keel

depth and sail height.

The model employs the Canadian Ice Service (CIS) iceberg model, which is included in

as library file. That library is linked to Fortran 90 files of the input, output, and user

variables. The model, thus, makes use of all the functionality of the CIS model. Drift

calculations consider forces resulting from water drag, air drag, wave radiation pressures,

and water pressure gradient. Added mass and Coriolis force are considered in the

equations. The processes which contribute to mass loss are surface melting due to solar

radiation, buoyant vertical convection, forced convection of water and air, wave erosion

and calving.

This report documents the code of the Local Iceberg Drift Model. Details of the

formulation of the full model are included in Appendix A. Listing of the code of the

Local Model is given in Appendix B.

HYD-TR-042 1

2. ORGANIZATION OF THE PROGRAM

Figure 1 shows the main subroutines of the program. The main program starts the

forecast. Definitions of the variables that are employed by the user are included in the

“userVariables” file. The input file provides run parameters, initial size and location of

the iceberg, water current and wind values, and various properties of ice and water.

Default values are included for those properties. The library conducts the calculations

that updates the iceberg velocity, position and size. The output file contains Fortran

statements that the user can customize to print the required results.

The program consists of four Fortran files and two binary files as follow,

Main.f90

userInput.f90

userOutput.f90

userVariables.f90

localBergLib.lib

variables.mod

Figure 1: Data flow diagram showing the main subroutines of the program.

HYD-TR-042 2

2.1 USER’S VARIABLES

The user variables are included in a module. It is named Module userVariables, and is

contained in the file “userVariables.f90”. Those variables, which are accessed by the

user, consist of:

Run parameters

Name Type Description

userNsteps integer Number of time steps

userDelt real Time step (s)

userPrintFreq integer Output frequency (steps)

Iceberg initial conditions


userBergLength real Mean length of the iceberg at waterline (m)

userLong real Longitude of the iceberg (degrees)

userLat real Latitude of the iceberg (degrees)

userU real Velocity along the East direction (m/s)

userV real Velocity along the North direction (m/s)

userTabularGeometry integer 1= Tabular, 0= non-tabular geometry

userKeelSailInput integer 1= yes (must be 1 if Tabular), 0= use default value.

This variable determines if the user will override the

default values of keel depth and sail height. It should be

"1" for tabular icebergs. For non-tabular icebergs, it

may be "1" to enter user values, or "0" to use default

values.

userKeelDepth real If "userKeelSailInput= 1", enter depth (m)

userSailHeight real If "userKeelSailInput= 1", enter sail height (m)

HYD-TR-042 3

Environmental variables


userUwind real array Wind velocity along the East direction (m/s) (i.e. East

component of wind velocity) - positive towards the East

userVwind real array Wind velocity along the North direction (m/s) (i.e. North

component of wind velocity) - positive towards the North

userUcur real array Water current along the East direction for each layer (m/s)

(i.e. East component of water current)

userVcur real array Water current along the North direction for each layer (m/s)

(i.e. North component of water current)

userWaterTemp real Water temperature (°C)

userWaveHeight real Height of wind waves (m)

userWavePeriod real Period of wind waves (s)

Material properties


userCdwat real Drag coefficient of water

userCdair real Drag coefficient of air

userRhoice real Density of ice (kg/m3)

userRhoair real Density of air (kg/m3)

userRhowat real Density of water (kg/m3)

userKwater real Thermal conductivity of water (W/m/(°C)

userKair real Thermal conductivity of air (W/m/(°C)

userNuwater real Kinematic viscosity of water (m2/s)

userNuair real Kinematic viscosity of air (m2/s)

userLatentHeat real Latent heat of fusion (J/kg)

userAlbedo real Albedo for icebergs

The model includes default values for each variable. These values can be found in the

“userInput.f90” file of the program. The user can either use these in case the real-time

data are not available or can input his own observed data. In this file user can also specify

the time step at which the program is executed (interval at which the calculations are

performed), the duration of the run, and output frequency (the interval at which the

variables of interest are recorded). In the “userOutput.f09” file the user can specify the

values of variables that are of interest to be recorded.

In general the program consists of four Fortran files: mail.f90, userInput.f90,

userOutput.f90, and userVariables.f90. The content of these files is listed in the

Appendix B.

HYD-TR-042 4

3. SUMMARY

This report documents the computer code of a Local iceberg drift and deterioration

model. The main (global) model, Iceberg Drift model, runs on the Canadian Ice Service

(CIS) main computer system. The end-users indicated an interest in having the ability to

run the model locally and use their experience, knowledge and real-time data. This would

enhance the accuracy of the forecast.

The code allows the user to customize the input and output and use their own

observations and data. The full CIS model is packaged in a library that is called by the

user. Thus the user has the access to the full functionality of the CIS model, while having

flexibility of using locally available information.

4. ACKNOWLEGEMENT

The financial support of the Program on Energy Research and Development (PERD) is

gratefully acknowledged.

HYD-TR-042 5

HYD-TR-042 6

APPENDIX A

Operational Model of Iceberg Drift

HYD-TR-042 7

HYD-TR-042 8

APPENDIX B

Fortran Files

HYD-TR-042 9

File: main.f90

!****************************************************************************

!

! PROGRAM: Local Iceberg Dynamics and Deterioration (LIDD)

!

! PURPOSE: The program keeps track of icebergs.

! The program performs the following calculations:

! - iceberg drift

! - iceberg melt

! - iceberg calving

!

! DESCRIPTION: Methodology of the calculations is given in the paper by:

! I.Kubat, M.Sayed, S.B.Savage and T. Carrieres

! "An operational model of iceberg drift"

! International Journal of Offshore and Polar Engineering

! Vol.15, No.2, June 2005, pp125-131

!

! INPUT FILES: userInput.f90

!

! OUTPUT FILES: userOutput.f90

!

! AUTHORS: Mohamed Sayed

! Canadian Hydraulics Centre

! National Research Council, Ottawa, Ontario K1A 0R6

! E-mail: [email protected]

! Tel (613)990-6958 Fax (613)952-7679

!

! AND

!

! Ivana Kubat

! Canadian Hydraulics Centre

! National Research Council, Ottawa, Ontario K1A 0R6

! E-mail: [email protected]

! Tel (613)993-7695 Fax (613)952-7679

!

! HISTORY:

! Version Date Comment

! ------- ---- -------

! 1.0 April 2006 Original code. M. Sayed & I. Kubat

!

!

!****************************************************************************

program main

use variables

implicit none

call runProgram

end program main

!****************************************************************************

File: userInput.f90

!************************************************************************************

subroutine userInput

!

!

! PURPOSE: - get values of the environmental input at time time step i.

! The input consists of water current, wind velocity,

! wind waves, and water surface temperature.

!

! DESCRIPTION: The input consists of:

! -Wind velocity along the east and north directions

! -Current for each time step along (towards) the east and north direction

! -Wind wave height and period

! -Temperature of surface water

!

!

!

!

!

! AUTHOR: Mohamed Sayed

!

!

! HISTORY:


! ------- ---- -------


!

!**************************************************************************************

use variables

use userVariables

implicit none

integer i

!Example test case

! Run parameters

userNsteps= 3390 !Number of time steps

userDelt= 120 !Time step (s)

userPrintFreq= 15 !Output frequency (steps)

!Initial iceberg variables

userBergLength= 100 ! Waterline length of the iceberg

userLong= 55.0 ! Longitude (degrees)

userLat= 50.0 ! Latitude (degrees)

userU= 0.0 ! East velocity component (m/s)

userV= 0.0 ! North velocity component (m/s)

!Geometry

userTabularGeometry= 0 ! 1= Tabular, 0= non-tabular geometry

userKeelSailInput= 1 ! 1= yes (must be 1 if Tabular), 0= use default value

! This variable determines if the user will override

! the default values of keel depth and sail height

! It should be "1" for tabular icebergs.

! For non-tabular icebergs, it may be "1" to enter

! user values, or "0" to use default values.

userKeelDepth= 70.0 ! If "userKeelSailInput= 1", enter depth (m)

userSailHeight= 10.0 ! If "userKeelSailInput= 1", enter sail height (m)

!Environmental forcing

userWaterTemp= 11.9 !Water temperature degrees C

userWaveHeight= 1.5 !Wind wave height (m)

userWavePeriod= 9.0 !Wind wave period (s)

!Current and wind values for each time step. The values could be constant

!or may be, for example, read from a file. The following loop can be replaced

!with the user.

do i= 1, userNsteps

userUcurrent(i)= 0.5 !East component of water current

userVcurrent(i)= 0.2 !North component of water current

userUwind(i)= 5.0 !East component of wind velocity (positive towards the East)

userVwind(i)= 7.5 !North component of wind velocity (positive towards the North)

end do

!Properties (default values are listed below)

userCdwat= 1.3 !Drag coefficient of water

userCdair= 1.9 !Drag coefficient of air

userRhoice= 910. !Density of ice (kg/m^3)

userRhoair= 1.3 !Density of air (kg/m^3)

userRhowat= 1030. !Density of water (kg/m^3)

userKwater= 0.562 !Thermal conductivity of water (W/m/degreeC)

userKair= 0.0241 !Thermal conductivity of air (W/m/degreeC)

userNuwater= 1.79E-06 !Kinematic viscosity of water (m^2/s)

userNuair= 1.32E-05 !Kinematic viscosity of air (m^2/s)

userLatentHeat=3.34E05 !Latent heat of fusion (J/kg)

userAlbedo= 0.7 !Albedo

end subroutine userInput

!************************************************************************************

File: userOutput.f90

!************************************************************************************

subroutine userOutput(step)

!

!

! PURPOSE: - Ouput the results.The subroutine is called at intervals

! defined by the user. The interval between outputsis in seconds is:

! interval = userPrintFreq * userDelt

!

!

!

!

!

!

!


!

!

! HISTORY:


! ------- ---- -------


!

!**************************************************************************************

use variables

use userVariables

implicit none

real:: time

integer, intent(in):: step

time= step* userDelt

! The user can open and close output files and record the values of

! variables of interest.

! For example:

! time = time from the start of the forecast (s)

! userLong = Longitude of the iceberg (degrees)

! userLat = Latitude of the iceberg (degrees)

! userU = East component of iceberg velocity (m/s)

! userV = North component of iceberg velocity (m/s)

! userBergLength = Waterline length of the iceberg

!Example test case

print *,time, userLong,userLat,userU,userV,userBergLength

end subroutine userOutput

!************************************************************************************

File: userVariables.f90

!************************************************************************************

Module userVariables

!

!

! PURPOSE: - Declaration of user variables

!

!

!

!

!

!

!


!

!

! HISTORY:


! ------- ---- -------


!

!**************************************************************************************

! Run parameters

integer:: userNsteps !Number of time steps

real:: userDelt !Time step (s)

integer:: userPrintFreq !Output frequency (steps)

!Initial iceberg variables

real:: userBergLength !Mean length of the iceberg at waterline (m)

real:: userLong !Longitude of the iceberg (degrees)

real:: userLat !Latitude of the iceberg (degrees)

real:: userU !Velocity along the East direction (m/s)

real:: userV !Velocity along the North direction (m/s)

integer:: userTabularGeometry !1= Tabular, 0= non-tabular geometry

integer:: userKeelSailInput ! 1= yes (must be 1 if Tabular), 0= use default value

! This variable determines if the user will override

! the default values of keel depth and sail height

! It should be "1" for tabular icebergs.

! For non-tabular icebergs, it may be "1" to enter

! user values, or "0" to use default values.

real:: userKeelDepth !If "userKeelSailInput= 1", enter depth (m)

real:: userSailHeight !If "userKeelSailInput= 1", enter sail height (m)

!Environmental forcing

real:: userWaterTemp !Water temperature degrees C

real:: userWaveHeight !Wind wave height (m)

real:: userWavePeriod !Wind wave period (s)

!Dimsnsion of the variables below should be equal or larger than the

!number of time steps "userNsteps".

real, dimension(20000):: userUcurrent,userVcurrent !East and North component of water current, respectively

real, dimension(20000):: userUwind,userVwind !East and North component of wind velocity, respectively

!Properties

real:: userCdwat,userCdair !Drag coefficients of water and air

real:: userRhoice !Density of ice (kg/m^3)

real:: userRhoair !Density of air (kg/m^3)

real:: userRhowat !Density of water (kg/m^3)

real:: userKwater !Thermal conductivity of water (W/m/degreeC)

real:: userKair !Thermal conductivity of air (W/m/degreeC)

real:: userNuwater !Kinematic viscosity of water (m^2/s)

real:: userNuair !Kinematic viscosity of air (m^2/s)

real:: userLatentHeat !Latent heat of fusion (J/kg)

real:: userAlbedo !Albedo

end module userVariables

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